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MA_775_DIABLO [31]
2 years ago
5

5. Consider the process where nA mol of gas A initially at 1 bar pressure mix with nB mol of gas B also at 1 bar to form 1 mol o

f a uniform mixture of A and B at a final total pressure of 1 bar, and all at constant temperature T. Assume that all gases behave ideally. a. Show that the entropy change, mixSm, for this process is given by mixSm
Chemistry
1 answer:
aalyn [17]2 years ago
8 0

Answer:

ΔSmix,m = 5.7628 J/K.mol

Explanation:

mix: A + B

∴ nA = x mol A

∴ nB = y mol B

⇒ n mix = x + y = 1 mol

∴ P total = 1 bar

∴ T: constant

entropy of gases when mixing:

  • ΔSmix = - nA*R*LnXA - nB*R*LnXB

∴ XA = x/1 = x

∴ XB = y/1 = y

⇒ ΔSmix = - x*R*Lnx - y*R*Lny

assuming: x = y = 0.5 mol

⇒ ΔSmix = - (0.5)(R)(- 0.693) - (0.5)(R)(- 0.693)

⇒ ΔSmix = (0.3465)(R) + (0.3465)(R)

⇒ ΔSmix = (0.6931)(R)

∴ R = 8.314 J/K.mol

⇒ ΔSmix,m = (0.6931)(8.314 J/K.mol)

⇒ ΔSmix,m = 5.7628 J/K.mol

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theoretical yield of the reaction is 121.38 g of NH₃ (ammonia)

limiting reactant is N₂ (nitrogen)

excess reactant is H₂ (hydrogen)

Explanation:

We have the following chemical reaction:

N₂ + 3 H₂ → 2 NH₃

Now we calculate the number of moles of each reactant:

number of moles = mass / molar weight

number of moles of N₂ = 100 / 28 = 3.57 moles

number of moles of H₂ = 100 / 2 = 50 moles

From the chemical reaction we see that 3 moles of H₂ are reacting with 1 moles of N₂, so 50 moles of H₂ are reacting with 16.66 moles of N₂ but we only have 3.57 moles of  N₂ available, so the limiting reactant will be N₂ and the excess reactant will be H₂.

Knowing the chemical reaction and the limiting reactant we devise the following reasoning:

if          1 mole of N₂ produce 2 moles of NH₃

then    3.57 moles of N₂ produce X moles of NH₃

X = (3.57 × 2) / 1 = 7.14 moles of NH₃

mass = number of moles × molar weight

mass of NH₃ = 7.14 × 17 = 121.38 g

theoretical yield of the reaction is 121.38 g of NH₃

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